Solve the equation for the red variable.
2 answers:
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<h3>Answer:</h3>
- using y = x, the error is about 0.1812
- using y = (x -π/4 +1)/√2, the error is about 0.02620
The actual value of sin(π/3) is (√3)/2 ≈ 0.86602540.
If the sine function is approximated by y=x (no error at x = 0), then the error at x=π/3 is ...
... x -sin(x) @ x=π/3
... π/3 -(√3)/2 ≈ 0.18117215 ≈ 0.1812
You know right away this is a bad approximation, because the approximate value is π/3 ≈ 1.04719755, a value greater than 1. The range of the sine function is [-1, 1] so there will be no values greater than 1.
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If the sine function is approximated by y=(x+1-π/4)/√2 (no error at x=π/4), then the error at x=π/3 is ...
... (x+1-π/4)/√2 -sin(x) @ x=π/3
... (π/12 +1)/√2 -(√3)/2 ≈ 0.026201500 ≈ 0.02620
a) The linear function that models the amount of water after t minutes is given by:
b) It takes 92 minutes to completely fill the pond.
Item a:
- Initially, the pond contains 200 gal of water, that is, the linear function has a y-intercept of 200.
- Filled at a rate of 12 gallons per minute, thus the linear function has a slope of 12.
Then, the function is:
Item b:
It takes t minutes to fill the pond, t is found for which:
Then
It takes 92 minutes to completely fill the pond.
A similar problem is given at brainly.com/question/16302622